Problem #2004

2004.

Carl decided to fence in his rectangular garden. He bought fence posts, placed one on each of the four corners, and spaced out the rest evenly along the edges of the garden, leaving exactly yards between neighboring posts. The longer side of his garden, including the corners, has twice as many posts as the shorter side, including the corners. What is the area, in square yards, of Carl’s garden?

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Instructions for entering answers:

Reduce fractions to
lowest terms and enter in the form 7/9.

Numbers involving pi should be written as 7pi or 7pi/3
as appropriate.

Square roots should be written as sqrt(3),
5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.

Exponents should be entered in the form 10^10.

If the problem is multiple choice, enter the appropriate
(capital) letter.

Enter points with parentheses, like so: (4,5)

Complex numbers should be entered in rectangular form
unless otherwise specified, like so: 3+4i. If there is no
real component, enter only the imaginary component (i.e. 2i,
NOT 0+2i).